Forward contracts

Such a market for trading chemical contracts would effectively help the industry separate the risk of asset ownership from both production and financial risk. Imagine, for example, if a pure commodity player could conclude forward contracts to lock in the price on most of its output volume and input raw materials. It could outsource the sales and logistics process to efficient transactional market makers and low cost logistics speciahsts, leaving it to focus purely on being distinctive in low cost operations. 

Consider the hypothetical interest rate swap nsed earlier to illustrate a swap. Let s look at party X s position. Party X has agreed to pay 10% and receive 6-month EURIBOR. More specifically, assuming a 50 million notional amount, X has agreed to buy a commodity called 6-month EURIBOR for 2.5 million. This is effectively a 6-month forward contract where X agrees to pay 2.5 million in exchange for deliv-... 

Consequently, interest rate swaps can be viewed as a package of more basic interest rate derivative instruments—forwards. The pricing of an interest rate swap will then depend on the price of a package of forward contracts with the same settlement dates in which the underlying for the forward contract is the same reference rate. 

As we have seen, interest rate swaps are valued using no-arbitrage relationships relative to instruments (funding or investment vehicles) that produce the same cash flows under the same circumstances. Earlier we provided two interpretations of a swap (1) a package of futures/forward contracts and (2) a package of cash market instruments. The swap spread is defined as the difference between the swap s fixed rate and the rate on the Euro Benchmark Yield curve whose maturity matches the swap s tenor. 

Spread forwards may be used by investors who wish to implement an investment strategy based on its view on movements in spreads. Exhibit 21.7 shows the cash flows under a credit spread forward. Exhibit 21.8 illustrates the use of a credit spread forward contract. 

Pt = the spot price of the underlying asset at the time of delivery X = the delivery price specified in the forward contract T = the term to maturity of the contract, in years, also referred to as the time to delivery... 

The payout yield, R, is the percentage of the spot price that is paid out at contract expiry, i.e., R = Pt-X) / Pt- The forward contract terms are set so that the present value of the payout Pj - X) is zero. This means that the forward price, F, on day one of the contract equals X (Note that the forward price is not the same as the value of the contract, which at this point is zero.) From the initiation of the contract until its expiration, the value ofXremains fixed. The forward price, F, however, fluctuates, generally rising and falling with the spot price of the underlying asset. 

FIGURE 6.1 shows the daily cash flows for a forward and a futures contract having identical terms. The futures contract generates intermediate cash flows the forward doesn t. As with the forward contract, the delivery price specified in the futures contract is set so that at initiation, the pres-... 

For the strategy employing forwards, contracts are bought, where r is the daily return (or instantaneous money market rate) and T the maturity term in days. The start forward price sF=X, and the payoff on expiry... 

This is also the payoff from the forward contract strategy. The key point is that if equation (6.3) below holds, then so must (6.4). 

The forward strategy can be used to imply the forward price, provided that the current price of the underlying and the money market interest rate are known. FIGURE 6.2 illustrates how this works, using the one-year forward contract whose profit/loss profile is graphed in figure 6.1 and assuming an initial spot price, P, of 50, a risk-free rate, r, of 1.05 percent, and a payout yield, R, of 1 percent. 

FIGURE 6.2 Forward Contract Profit/Loaa Profiln ... 

The price of the forward contract is thus a function of the current underlying spot price, the risk-free or money market interest rate, the payoff, and the maturity of the contract. It can be shown that neither F > P r/l(f nor F

futures price is at fair value. 

In 1976 Fisher Black presented a slightly modified version of the B-S model, using similar assumptions, for pricing forward contracts and interest rate options. Banks today employ this modified version, the Black model, to price swaptions and similar instruments in addition to bond and interest rate options, such as caps and floors. The bond options described in this section are options on bond futures contracts, just as the interest rate options are options on interest rate futures. 

The Black model refers to the underlying assets or commodity s spot price, S t). This is defined as the price at time t payable for immediate delivery, which, in practice, means delivery up to two days forward. The spot price is assumed to follow a geometric Brownian motion. The theoretical price, F t,T), of a futures contract on the underlying asset is the price agreed at time t for delivery of the asset at time T and payable on delivery. When t= T, the futures price equals the spot price. As explained in chapter 12, futures contracts are cash settled every day through a clearing mechanism, while forward contracts involve neither daily marking to market nor daily cash settlement. 

The values of forward, futures, and option contracts are all functions of the futures price F(t,T), as well as of additional variables. So the values at time r of a forward, a futures, and an option can be expressed, respectively, asf F,t), u F,t), and C F,i). Since the value of a forward contract is also a function of the price of the underlying asset S at time T, it can be represented hy f F,t,S,T). Note that the value of the forward contract is not the same as its price. As explained in chapter 12, a forward s price, at any given time, is the delivery price that would result in the contract having a zero present value. When the contract is transacted, the forward value is zero. Over time both the price and the value fluctuate. The futures price... 

Because futures contracts are repriced each day at the new forward price, their prices imply those of forward contracts. When F rises, so that F>S,f is positive when T" falls, / is negative. When the contract expires and delivery takes place, the forward contract value equals the spot price minus either the contract price or the spot price, futures price equals the spot price, and the value of the forward contract equals the spot price minus the contract price or the spot price. 

Setting T = T-rand using (8.32) and (8.33), an equation can be created for deriving the fair value of a commodity option or option on a forward contract, shown as (8.35). 

Jarrow, R., and G. Oldfield. 1981. Forward Contracts and Futures Contracts. Journal of Financial Economics 9, December, 373—382. 

In West Germany there is a completely free market with no regulation of production and no control of price. Growers make forward contracts for most of their crop with merchants who collect hops from the farm. 

In the United States, the Hops Administrative Committee controls production but not price. Each grower has a basic quota and an annual quota based on the prospect of total sales. Most prices are negotiated as forward contracts between the grower and the dealer on one hand and between the dealer and the brewer on the other. American hop farms are much larger than their European counterparts and their production costs are undoubtedly lower. 

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